Quantitative Evidence to Challenge the Traditional Model in Heterogeneous Catalysis: Kinetic Modeling for Ethane Dehydrogenation over Fe/SAPO-34

The production of ethylene from ethane dehydrogenation (EDH) is of great importance in the chemical industry, where zeolites are reported to be promising catalysts and kinetic simulations using the energetics from quantum mechanical calculations might provide an effective approach to speed up the development. However, the kinetic simulations with rigorous considerations of the zeolite environment are not yet advanced. In this work, EDH over Fe/SAPO-34 is investigated using quantum mechanical calculations with kinetic simulations. We show that an excellent agreement between the reaction rates from the self-consistent kinetic simulations using the coverage-dependent kinetic model developed in this work and the experimental ones can be achieved. We demonstrate that the adsorbate–adsorbate interactions are of paramount importance to the accuracy of kinetic calculations for zeolite catalysts. Our self-consistent kinetic calculations illustrate that the CH3CH2• radical rather than CH3CH2* is a favored intermediate. Perhaps more importantly, we reveal that the traditional model to describe catalytic reactions in heterogeneous catalysis cannot be used for the kinetics of the system and it may not be appropriate for many real catalytic systems. This work not only builds a framework for accurate kinetic simulations in zeolites, but also emphasizes an important concept beyond the traditional model.

. Diagrams of energy changes from the initial states to the final states over Fe/SAPO-34: (a) for R3 with H0 and (b) R3 with H1, where H0 and H1 refer to the numbers of 1 and 2 adsorbed H* on the acid sites, respectively. The transition states (TS) of R4 were determined by the constrained optimization, resulting in an energy barrier at 0 K. However, no free energy barrier was found after the free energy correction at 873 K.      . Flow chart for the scheme of the coverage-dependent microkinetic modelling, where ! and " represent the initial setting coverage and the coverage calculated from self-consistent microkinetic modelling. X represents the convergence, namely the difference between the initial setting coverage and the calculated one (X = 0.01 in this work). 1 Microkinetic modelling was conducted in this work through CATKINAS. 2,3 Figure S10. Formation rates of ethyl radical and CH2CH2 as a function of ethyl radical pressure over SAPO-34. To determine the CH3CH2• pressure at the steady state, kinetic calculations based on a series of the CH3CH2• pressures were conducted. A linear relation was found between the consumption/production rate and the pressure. The CH3CH2• pressure at the equilibrium of consumption and production can be obtained, at which the net rate of CH3CH2• is equal to 0.  Here, the magnitude of the degree of rate control of each elementary reaction reflects the relative degree of the elementary reaction in controlling the rate of the overall reaction. Figure S13. Comparison between estimated experimental reaction rates (red, see Note 2 below) and theoretical reaction rates (blue) with the temperatures from 800 to 950 K. It is noted that the theoretical simulations overestimate the activity at high temperatures. However, the scale of TOF is very small and hence the differences are small.  Tables   Table S1. Adsorption energies (eV) of ethane over Fe/SAPO-34 and SAPO-34.

R4
CH3CH2* → CH2CH2(g) + H* 2.14 × 10 -11 R5 2H* → H2(g) + 2* 5.92 × 10 -1   Table S11. Parameters of the linear curves in Figure 4a for Fe/SAPO-34 and Figure S6 for SAPO-34.   Table S13. Elementary steps for EDH over SAPO-34 with free energy corrections ∆ #$% at different H-covered coverages, where * represents an active site, and CH3CH2• represents a CH3CH2 radical, i of Hi refers to the number of adsorbed H* initially on the acid sites, / refers to no additional reaction barriers, the energy changes from the initial states to the final states are displayed in Figure S3.

Note 1: Thermodynamic Corrections
The standard equations were used to perform the thermodynamic corrections, namely the free energy corrections, considering the zero-point energy (ZPE), thermal energy and entropy. 4,5 Only vibrational motions were included for any surface species. The ZPE correction is calculated by: where ℎ is the Plank's constant, and ) is the vibrational frequency calculated using the harmonic oscillator approximation. The standard vibrational thermal energy is calculated by: where is the gas constant, and 2 is the Boltzmann's constant. The standard vibrational entropy is calculated as follows: The free energies for adsorbates were corrected by the following the equation: The standard Gibbs free energy ( $ ) are calculated as follows: $ = 4$4!5 + ∆ #$% (S5) where 4$4!5 refers to the total energy from DFT calculations. In addition, the thermodynamic corrections for any species in the gas phase were obtained by Gaussian code. 6 Moreover, we employed an approximation that the species in the channel of zeolite without adsorption retains 2/3 of the translational entropy of its ideal gas, which was a common practice in previous work. 7 The free energy corrections ∆ #$% are shown in Table S12, S13 above.

Note 2: Experimental TOF estimation
The experimental rate of CH2CH2 on FeS-1-EDTA was evaluated using the standard TOF formula. The total active sites in the zeolite with the Fe loading of catalyst (m, 0.2 g of catalyst with Fe loading at 0.8 wt%) can be obtained as: where M and n refer to the relative atomic mass of iron and the total active sites in one unit cell from the modelling (n = 4 for FeS-1-EDTA in this work due to the local structure). The TOF at 1s was calculated by gas flowing rate (R) of 2 L gcat -1 h -1 (30% ethane balanced with Ar) and the conversion (X): where 6 and refer to the Avogadro constant and the standard molar volume of a gas.

Note 3: Explanation that the TOF value increases with respect to temperature rise
The first elementary step of the reaction, namely the first step dehydrogenation of ethane, is the step from ethane in the gas phase to CH3CH2•. When the temperature increases, a larger entropy effect in the free energy correction (-TS) can be expected on the ethane in the gas phase than that in the transition state due to the larger degree of freedom (entropy) of the gaseous ethane. Therefore, the energy difference between the transition state and initial state increases, leading to the barrier increase as the temperature increase.
The rate increase can be explained from the Arrhenius equation with the temperature increase: The reaction barriers calculated at the temperatures of 800 K and 950 K are 899: = 2.34 and ;<9: = 2.58 , respectively. Substituting them into the equation, we can obtain that the exponential term ( 0( -73 ) at 800 K (-3.39 × 10) is smaller than that at 950 K (-3.15 × 10), illustrating that when the temperature increases, the TOF will increase.